A comparative study of Stochastic and Deterministic Population Models

In this paper theory from population biology is combined with stochastic differential equations. The aim is to compare previously studied deterministic population models with corresponding stochastic population models. As an illustrative example the models are applied to a classical dataset (Gause, 1934). The first half of the paper gives a brief review of the theoretical background needed in order to understand the subsequent analysis. This review begins with some mathematical concepts, followed by concepts in population biology and ends with statistical theory, e.g. stochastic processes and stochastic differential equations. The second half of the paper deals with the results of the analysis and the subsequent discussion. In the analysis the deterministic models and the stochastic models are discussed and compared. Since the stochastic models capture stochastic fluctuations in populations they give a more accurate picture of reality. On the other hand, question marks still remain concerning the best way of expressing the stochastic models. Furthermore it would be interesting to apply the new stochastic models to data from wild life populations and not on data from laboratory populations (as was the case here).